Local convergence of tensor methods

Nikita Doikov () and Yurii Nesterov ()
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Nikita Doikov: Université catholique de Louvain, ICTEAM
Yurii Nesterov: Université catholique de Louvain, LIDAM/CORE, Belgium

No 3239, LIDAM Reprints CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. We justify local superlinear convergence under the assumption of uniform convexity of the smooth component, having Lipschitz-continuous high-order derivative. The convergence both in function value and in the norm of minimal subgradient is established. Global complexity bounds for the Composite Tensor Method in convex and uniformly convex cases are also discussed. Lastly, we show how local convergence of the methods can be globalized using the inexact proximal iterations.

Keywords: Convex optimization; High-order methods; Tensor methods; Local convergence; Uniform convexity; Proximal methods (search for similar items in EconPapers)
Pages: 22
Date: 2023-01-01
Note: In: Mathematical Programming, 2022, vol. 193(1), p. 315-336
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Persistent link: https://EconPapers.repec.org/RePEc:cor:louvrp:3239

DOI: 10.1007/s10107-020-01606-x

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